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Probability, explained with data
The core ideas behind every tool on this site — odds, independence, the fallacies people fall for, and how to test a claim honestly. Every page works through its ideas with numbers from the real dataset, not generic filler.
Basics
The odds of winning
How lottery jackpot odds are calculated, and why they are worse than they look.
Independence: why past draws don't matter
Each lottery draw is independent — the past cannot change the next draw's probabilities.
The law of large numbers
Why frequencies converge over millions of draws — and why that changes nothing about your next ticket.
Expected value
How to think about the true cost of a ticket: probability times prize, minus the price.
Combinations: how many ways?
The math of ticket counts, why order doesn't matter, and how big those numbers get.
Myths
The gambler's fallacy
Why an overdue number is not 'due' — the classic probability misconception, checked against real data.
Hot and cold numbers
Frequent and absent numbers are statistical noise, not signals — demonstrated with real and simulated history.
Clustering: why random looks non-random
Streaks, clusters, and repeating pairs are the fingerprints of randomness, not patterns to bet on.
Analysis
Multiple testing: seeing patterns everywhere
With thousands of numbers, pairs, and triples, some statistic will always look extreme — by chance.
Overfitting: when models fool themselves
A rule tuned on past data will always fit the past — the test is whether it survives the future.
Backtesting: testing strategies honestly
What a no-lookahead backtest can and cannot tell you about a selection strategy.
Statistical significance
What 'significant' actually means, why it is easy to fool, and how this site checks it.